Zobrazeno 1 - 10
of 187
pro vyhledávání: '"Top, Jaap"'
The aim of this paper is to present elliptic curves defined over function fields of even characteristic having arbitrarily large Mordell-Weil rank. More precisely, we study elliptic curves arising as quartic twist of a supersingular elliptic curve de
Externí odkaz:
http://arxiv.org/abs/2405.13408
Autor:
van der Put, Marius, Top, Jaap
There is an abundance of equations of Painlev\'e type besides the classical Painlev\'e equations. Classifications have been computed by the Japanese school. Here we consider Painlev\'e type equations induced by isomonodromic families of linear ODE's
Externí odkaz:
http://arxiv.org/abs/2404.15767
This exposition reviews what exactly Gauss asserted and what did he prove in the last chapter of {\sl Disquisitiones Arithmeticae} about dividing the circle into a given number of equal parts. In other words, what did Gauss claim and actually prove c
Externí odkaz:
http://arxiv.org/abs/2110.01355
Autor:
van der Put, Marius, Top, Jaap
Publikováno v:
SIGMA 19 (2023), 068, 26 pages
Isomonodromy for the fifth Painlev\'e equation ${\rm P}_5$ is studied in detail in the context of certain moduli spaces for connections, monodromy, the Riemann-Hilbert morphism, and Okamoto-Painlev\'e spaces. This involves explicit formulas for Stoke
Externí odkaz:
http://arxiv.org/abs/2107.07204
This paper discusses prime numbers that are (resp. are not) congruent numbers. Particularly the only case not fully covered by earlier results, namely primes of the form $p=8k+1$, receives attention.
Comment: 14 pages
Comment: 14 pages
Externí odkaz:
http://arxiv.org/abs/2105.01450
For the hyperelliptic curve C_p with equation y^2=x(x-2p)(x-p)(x+p)(x+2p) with p a prime number, we discuss bounds for the rank of its Jacobian over Q, find many cases having 2-torsion in the associated Shafarevich-Tate group, and we present some res
Externí odkaz:
http://arxiv.org/abs/2102.12977
Autor:
Groen, Steven R., Top, Jaap
Publikováno v:
INTEGERS (2022), volume 22, number 108
In this paper, we give explicit equations for homogeneous spaces corresponding to a rational isogeny of degree $3$. An explicit set of elliptic curves with elements of order $3$ in their Tate-Shafarevich group is constructed. Combining this gives exp
Externí odkaz:
http://arxiv.org/abs/2102.11737
Autor:
Top, Jaap
This note presents explicit equations (up to birational equivalence over $\mathbb{F}_2$) for a complete, smooth, absolutely irreducible curve $X$ over $\mathbb{F}_2$ of genus $50$ satisfying $#X(\mathbb{F}_2)=40$. In his 1985 Harvard lecture notes on
Externí odkaz:
http://arxiv.org/abs/1911.06209
Publikováno v:
In Finite Fields and Their Applications October 2023 91
Autor:
Djukanović, Martin, Top, Jaap
Publikováno v:
In Expositiones Mathematicae September 2023 41(3):566-576